ARBITRAGES BETWEEN DIFFERENT OPTIONS MARKETS

commodity futures and interest rate futures. It is not necessary here to go into the details of futures or options on futures and the interested reader is referred to the many excellent texts on the subject. The important point to note is that the options follow the same type of price curves discussed above. The real difference, however, between stock options and futures options is that of transaction costs.

When discussing the long or short volatility portfolios we left the question of transaction costs aside. We either ignored the costs or assumed that they were small. In reality this is sometimes not the case. In some stock markets the cost of dealing in the underlying can be non-trivial and this has implications for the volatility player. If the transaction costs associated with buying or selling the underlying are significant, then the volatility player must incorporate this into his rehedging strategy. If the costs are very high then the long volatility player must wait for a much larger move before rehedging.

The real virtue of trading volatility using options on futures is that the costs, in comparison to those of stocks, are extremely small. As an example, the bid to offer spread on the S&P 500 stock index future is typically 0.02%. Each time a hedger buys or sells a future he is paying away 0.02% of the underlying exposure. The same cost on say IBM stock would be 0.5% and on a typical UK stock such as BP may be as high as 2%. Transaction costs are usually a direct function of the liquidity and most stock index futures contracts are extremely liquid.

8.7 ARBITRAGES BETWEEN DIFFERENT OPTIONS MARKETS

From time to time situations arise that allow the volatility player to profit whatever the underlying market is doing. Because more and more individuals are looking at the derivative markets for these situations they are increasingly difficult to find, but they still do turn up. There are a number of markets where options on the same or a similar product are priced differently. Arbitrageurs typically buy cheap volatility in one market and simultaneously sell expensive volatility in the other.

Options on Stock Indexes versus Options on Stock Index Futures

In the USA there are a number of stock index related options. By far the largest are the options on the S&P 100 stock index and the options on the S&P 500 stock index futures contract. The two underlying stock indexes are highly (but not perfectly) correlated. Even when the two indexes are not perfectly correlated, the volatilities are usually very similar. This similarity in volatilities should be, and usually is, reflected in the relevant option prices. Occasionally, however, the implied volatilities in one market get out of line with those in the other market and when this occurs, arbitrageurs buy the cheap options and sell the expensive options.

Stock Index Options versus Individual Stock Options

Investing in a basket of stocks is, by definition, less risky than investing in an individual stock. The concept of portfolio diversification is well known. For risk we can of course read volatility and so one would expect the implied volatilities of stock index options to be lower than those of an individual stock option. This is indeed the situation in most markets. Furthermore, there is a well-defined mathematical relationship between the volatility of an index and the individual volatilities of the index constituents but occasionally this relationship is broken.

There occurs from time to time arbitrage opportunities when the stock index option implied volatilities get out of line with those of the individual stock option implied volatilities. These situations often occur in times of extreme market moves. In the 1987 stock market crash, the UK FTSE index options became extremely expensive as did the individual stock options. Although high, many of the individual options were priced the same as the index options and this was clearly an anomalous situation. Arbitrageurs purchased baskets of individual stock options and sold short index options. Within three weeks the portfolios were unwound with large profits.

I here are of course other risks in this strategy, the most obvious one being that the basket of stocks underlying the individual options is not a match for the index.

The FTSE stock index has 100 constituents ,ind only 60 of these have stock options. The arbitrage trade should only he instigated when the anomalous option pricing is large enough u> cover any losses associated with mistracking the index.

Japanese Warrants versus Japanese Stock Index Futures

In section 8.2 we mentioned the large profits made, until recently, in the Japanese warrant market. Eventually, more and more hedgers discovered the anomalous price behaviour and everyone got involved in the business of borrowing stock for short selling. Selling stock short is a much more complicated business in Japan than other developed markets. One complication is that associated with stock registration. Most Japanese stock holders have to register details of ownership to the Japanese Ministry of Finance at least once a year and in some cases twice a year. This meant that many volatility players long a warrant and short the underlying were often forced to unwind the trade in order to return stock to the owners for registration. These and other complications made life difficult for the warrant hedger. In fact many market participants believe that these very complications were responsible for the initial abundance of cheap warrants. Over time hedgers gradually found ways round these difficulties and managed to establish long-term agreements with stock-borrowing institutions. These agreements removed the need to periodically unwind trades and so successful hedges could be run for a full four or five years until warrant expiry.

Ftowever, there still existed a very large pool of warrants whose underlying stock was impossible to borrow. These warrants could not be hedged and not surprisingly, were the cheapest in the market. The advent of a liquid Japanese stock index futures market in the late 1980s changed the situation. More sophisticated hedgers managed to construct portfolios consisting solely of cheap warrants hedged with short stock index futures contracts. Using sophisticated statistical techniques, they derived special subsets of stocks underlying the cheap warrants that would track the relevant stock index. In this way the hedgers got around the short stock problem completely. In addition to establishing a good market hedge, there were a number of other advantages in using the stock index futures contract.

As mentioned before, the costs of dealing in futures are very small and offered a considerable advantage over dealing in stock. Liquidity was another major advantage. Many of the stocks underlying the cheap warrants were almost completely illiquid, whereas the Japanese stock index futures market become one of the most liquid in the world. The profits to the hedgers using stock index futures were enormous, but like everything else, the opportunity only lasted three to four years.